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Well-posedness and stability in set optimization with applications

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Abstract

This paper is about the well-posedness and stability in set optimization with applications to vector-valued games involving uncertainty. Some characterizations for several types of well-posedness with their relations in set optimization are given under mild conditions. Some sufficient and necessary conditions for these types of well-posedness in set optimization are also given by using the local C-Lipschitz continuity. Moreover, the upper semi-continuity, lower semi-continuity and compactness of minimal solution mappings are studied for parametric set optimization involving the cone Lipschitz continuous set-valued mapping. Finally, some obtained results are applied to derive the well-posedness for vector-valued games with uncertainty.

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Acknowledgements

The authors are grateful to the editor and the referees for their valuable comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Sichuan University, Chengdu, 610064, Sichuan, People’s Republic of China

    Chuang-liang Zhang & Nan-jing Huang

  2. School of Mathematics, Jiaying University, Meizhou, 514015, Guangdong, People’s Republic of China

    Chuang-liang Zhang

Authors
  1. Chuang-liang Zhang
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  2. Nan-jing Huang
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Correspondence to Nan-jing Huang.

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This work was supported by the National Natural Science Foundation of China (11471230, 11671282).

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Zhang, Cl., Huang, Nj. Well-posedness and stability in set optimization with applications. Positivity 25, 1153–1173 (2021). https://doi.org/10.1007/s11117-020-00807-0

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